UNA can't work properly without cron. So setting up cron properly from the very beginning is very essential.
It's not only upgrade relying on cron job, there are a lot of other things, which you can't see immediately.
I would suggest to ensure that cron jobs are setup and you shouldn't have problems with the upgrade.
Also we've started to show last cron execution time in Studio > Dashboard > Host Tools > Server Audit, it should be always within a minute from now, it will help to ensure that the cron is setup properly.
Thanks, Alex T⚜️! It seems like people still experienced strange behavior even after setting up the cron job correctly. For example, after I adjusted my cron job to run every minute, I clicked on upgrade, and the site still didn't upgrade after several minutes. Although I could see certain files like the splash page, did update. I had to click on upgrade one more time, then finally, everything updated.
By the way, the log showed that the upgrade was successful the first time. Even though it wasn't.
It's hard to say exactly what happened. Just sharing my experience.